Sure, let's solve the given mathematical expression step-by-step. The expression is:
[tex]\[
\frac{2}{4}+\frac{3}{6}+\left[\frac{4}{2}+\left\{\frac{2}{4}-\left(\frac{3}{4}+\frac{2}{4}\right)\right\}\right]
\][/tex]
Let's break it down and solve it step by step:
1. Calculate individual fractions:
[tex]\[
\frac{2}{4} = 0.5
\][/tex]
[tex]\[
\frac{3}{6} = 0.5
\][/tex]
[tex]\[
\frac{4}{2} = 2.0
\][/tex]
[tex]\[
\frac{2}{4} = 0.5
\][/tex]
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
[tex]\[
\frac{2}{4} = 0.5
\][/tex]
2. Calculate the innermost parentheses:
[tex]\[
\left(\frac{3}{4} + \frac{2}{4}\right) = 0.75 + 0.5 = 1.25
\][/tex]
3. Now, calculate the expression inside the curly brackets:
[tex]\[
\frac{2}{4} - 1.25 = 0.5 - 1.25 = -0.75
\][/tex]
4. Next, calculate the expression inside the square brackets:
[tex]\[
\frac{4}{2} + (-0.75) = 2.0 - 0.75 = 1.25
\][/tex]
5. Finally, sum all the results:
[tex]\[
\frac{2}{4} + \frac{3}{6} + \left(1.25\right) = 0.5 + 0.5 + 1.25 = 2.25
\][/tex]
So, the step-by-step solution for the expression [tex]\(\frac{2}{4}+\frac{3}{6}+\left[\frac{4}{2}+\left\{\frac{2}{4}-\left(\frac{3}{4}+\frac{2}{4}\right)\right\}\right]\)[/tex] is [tex]\(2.25\)[/tex].
